[EM] Re: Weak INI -- three possibilities

[Jobst Heitzig]

Here's an example where Tideman and the River method fail those
ICI/INI versions:

Relative strengths:
	...  beats ...
	|    A B X Y Z
	A      1 4 - -
	B    -   - - 5
	X    - 5   3 -
	Y    4 1 -   3
	Z    5 - 2 -

Since only X beats Y directly, there is no beatpath from X to Y through
Z. (Only beatpaths without loops can be meant, otherwise (at least when
winners belong to the Smith set) there would in general be a beatpath
from X to Z and one from X to Y which together with Z>X would combine to
a loopy beatpath from X to Y through Z...)

River method: A --5--> Z --5--> B --5--> *X* <--3-- Y
Tideman additionally adds Y>A,B,Z.
	
River method without Z: B --5--> X --4--> A --4--> *Y*
Tideman additionally adds Y,A>B.

However, although beatpaths are a wonderful construct from a
mathematical point of view, I'm not sure whether the existence of a
beatpath without a direct beat has that much significance to become part
of a meaningful condition...

Jobst